David,
> Re: Can one make localizing inferences when a cluster reaches
> significance but no voxels reach voxel-level significance?
I'll try to provide a short answer to your well-motivated question:
Yes.
In more detail...
> The SPM99 manual seems fairly clear, stating that the cluster level
> significance means that the size of the cluster exceeds that
> expected by chance.
Yes, that is the precise interpretation.
> Nothing is said about the cluster location. In Human Brain
> Function, page 91, it says that within a cluster, nothing can be
> said at the voxel level [yet] the interpretation of results will
> clearly be different depending on threshold.
I won't say 'nothing' can be said; when a cluster is significant we
know that *one* or more voxels within the cluster are significant, but
we don't know which ones.
> However, in NeuroImage 1996;4:223, nearly the last sentence says
> this example highlights the potential benefit of set-level
> inferences; in that the entire activation profile can be described
> anatomically and characterized as significant, therein providing a
> complete and comprehensive picture of activations ... (emphasis
> added).
Set-level inference, based on counting the number of clusters greater
than a given size, has less spatial specificity than cluster-level
inference. Just like cluster inference, you know the location of the
blobs, but set-level inference only tells you when you have a
suprisingly large number of blobs, not *which* blobs are suprisingly
large.
> In the SPM output, the cluster data are shown as the cluster size at the
> specified analytical threshold. No anatomical data are provided,
> although one can find the cluster on the glass-brain projections.
> Any statement about a specific anatomical location would seem to take the
> analysis further toward the voxel level. Thus, if a cluster
> achieves significant size and appears on the glass-brain images in a
> location that indicates a specific region of the brain, say the occipital
> lobe, can one say that the contrast utilized yields a significant
> difference in the occipital lobe? I would think not.
I think what you're running up against is a certain conditioning that
occurs in a cluster size test. In essence, given a
cluster-defining-threshold, we find clusters and essentially condition
on which voxels gave rise to a cluster. We then make inference on the
(random) cluster size and connect that to the (fixed) location of
voxels in the cluster. This is weird (though not a whole lot weirder
than classic inference, where we essentially condition on the observed
statistic value, and then compare it to all future experiments under
the null to get a P-value), and is why we don't have confidence
regions on where a cluster lives. None-the-less, we know which voxels
generated the cluster and hence know where to make the
one-or-more-voxels inference.
Does this help?
-Tom
-- Thomas Nichols -------------------- Department of Biostatistics
http://www.sph.umich.edu/~nichols University of Michigan
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-------------------------------------- Ann Arbor, MI 48109-2029
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